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An experiment to distinguish between diffusive and specular surfaces for thermal radiation in cryogenic gravitational-wave detectors

MetadataDetails
Publication Date2015-07-01
JournalProgress of Theoretical and Experimental Physics
AuthorsYusuke Sakakibara, Nobuhiro Kimura, T. Suzuki, K. Yamamoto, Chihiro Tokoku
InstitutionsThe University of Tokyo, Tohoku University
Citations1
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Technical Documentation and Analysis: Thermal Radiation Control using MPCVD Diamond

Section titled “Technical Documentation and Analysis: Thermal Radiation Control using MPCVD Diamond”

Paper Analyzed: An experiment to distinguish between diffusive and specular surfaces for thermal radiation in cryogenic gravitational-wave detectors (Prog. Theor. Exp. Phys. 2015, 073F01)


This documentation summarizes the experimental validation of surface reflection characteristics crucial for managing parasitic heat loads in advanced cryogenic gravitational-wave detectors (e.g., KAGRA).

  • Application Focus: Minimizing thermal radiation heat transfer through duct shields to maintain cryogenic operating temperatures (20 K) of main mirrors, thereby reducing thermal noise.
  • Core Challenge: Accurately determining if shield inner surfaces reflect thermal radiation diffusively or specularly, as specular reflection dramatically increases heat load (several orders of magnitude higher than diffusive).
  • Experimental Method: A novel setup measuring radiative heat transfer between a heated inner sphere (300 K down to 100 K) and a liquid nitrogen-cooled outer sphere (77 K) inside a high-vacuum chamber.
  • Material Tested: The spheres were coated with a 1 ”m thick Diamond-Like Carbon (DLC) layer applied over a surface polished to approximately 30 ”m roughness.
  • Key Finding: The DLC-coated surface exhibited specular reflection for thermal radiation, consistent with the radiation wavelength (~10 ”m) being significantly longer than the effective surface roughness.
  • Sales Value Proposition: 6CCVD provides MPCVD diamond materials and precision polishing (Ra < 1 nm) that guarantee superior specular or tailored diffusive performance required for ultra-low thermal noise, high-stability cryogenic systems.

Extraction of hard data points and key parameters from the experimental setup.

ParameterValueUnitContext
Inner Sphere MaterialOxygen-free CopperN/ADiameter: 30 mm, Mass: 127 g
Outer Sphere MaterialAluminum A1070N/ADiameter: 220 mm
Coating MaterialDiamond-Like Carbon (DLC)N/APromising vacuum-compatible candidate
Coating Thickness1”mApplied to both spheres
Buffing/Polishing LevelJIS #400N/AResulting roughness: ~30 ”m
Outer Sphere Temperature (Tn)77KMaintained by liquid nitrogen
Inner Sphere Max Temp (T)300KStart temperature
Experiment Vacuum Level< 10-3PaPrevents gas heat conduction
Thermal Wavelength (300 K)~10”mCharacteristic blackbody radiation peak
Thermal Power Ratio (Specular vs. Diffusive)Several Orders of MagnitudeN/ASpecular power >> Diffusive power (L/d = 50, high reflectivity)
Fitted DLC Emissivity ($\epsilon$)$0.3 \times (T / 300 K)$N/AFitted based on cooling curve (proportional to T)
Inner Sphere Position Shift5cmUsed to test dependence on reflection mode

A concise sequence of experimental steps used to distinguish specular from diffusive surfaces in a cryogenic, high-vacuum environment.

  1. Preparation and Coating: Oxygen-free copper (inner sphere) and Aluminum A1070 (outer sphere) components were fabricated, polished (JIS #400, resulting in ~30 ”m roughness), and coated with a 1 ”m thick DLC layer.
  2. Vacuum Setup: The inner sphere was suspended within the outer sphere (vacuum chamber) using nylon wire. The system was evacuated to < 10-3 Pa to eliminate heat transfer via gas conduction and prevent water condensation.
  3. Cryogenic Cooling: The outer sphere was immersed in liquid nitrogen, maintaining its temperature at the boiling point of 77 K.
  4. Heat Transfer Measurement: The temperature (T) of the inner sphere was monitored over time using a calibrated thermometer (DT-670-CU).
  5. Cooling Rate Derivation: The radiative heat transfer (Q) absorbed by the outer sphere was derived from the inner sphere’s cooling speed (dT/dt) using the specific heat capacity of copper, $Q = -MC(T) (dT/dt)$.
  6. Positional Testing: Measurements were performed with the inner sphere centered and subsequently shifted vertically by 5 cm. Specular reflection results in position-dependent heat transfer, while diffusive reflection results in position-independent heat transfer.
  7. Comparison and Fitting: Experimental cooling curves were compared against Monte Carlo ray-tracing simulations for both purely specular and purely diffusive surface models to confirm the DLC surface’s specular nature and derive its emissivity.

This experiment confirms that achieving precise control over thermal radiation reflection (either perfectly specular or reliably diffusive) requires highly controlled surface engineering. 6CCVD specializes in providing MPCVD diamond materials that exceed the surface finish requirements of this research, offering a path to replicability and performance extension for gravitational-wave detector projects like KAGRA.

To replicate the ultra-stable thermal environment and achieve superior surface quality required for these detectors, 6CCVD recommends the following:

  • Optical Grade SCD (Single Crystal Diamond): Ideal for primary mirror substrates or reflective elements requiring the lowest possible thermal noise and highest degree of specular reflection.
    • Advantage: Unmatched purity and thermal conductivity at cryogenic temperatures.
    • Surface Guarantee: Achieves Ra < 1 nm polishing, offering a truly optically flat, specular surface far surpassing the ~10 ”m roughness examined in this paper.
  • Engineering Grade PCD (Polycrystalline Diamond): Perfect for structural elements, baffles, or duct shields where high thermal stability and customizable large areas are critical.
    • Advantage: Available in plates/wafers up to 125 mm diameter, allowing for integration into large-scale cryogenic systems.
    • Customization Potential: Can be utilized for highly thermally stable baffles designed to suppress specular reflection, as suggested by the researchers.

The experiment highlights the necessity of integrating specialized coatings and complex geometries (e.g., baffles). 6CCVD’s in-house capabilities directly address these engineering requirements:

  • Custom Dimensions and Geometries: We supply MPCVD diamond plates and wafers up to 125 mm diameter (PCD) and offer comprehensive laser cutting services to produce complex shapes, such as the annular baffles or custom shield components needed for duct shields.
  • High-Quality Polishing: While the paper used a 30 ”m polish, critical applications demanding true specular behavior must achieve roughness significantly smaller than the relevant 10 ”m thermal wavelength. Our standard service offers Ra < 1 nm (SCD) and Ra < 5 nm (PCD) on inch-size wafers, guaranteeing predictable, high-fidelity specular reflection necessary for precise thermal modeling.
  • Metalization Services: 6CCVD can deposit custom reflective or absorptive layers directly onto diamond substrates via our internal metalization capability, including: Au, Pt, Pd, Ti, W, and Cu. This allows researchers to engineer specific emissivity and reflectivity properties beyond the scope of a standard DLC coating.

6CCVD’s in-house PhD team provides expert consultation on material selection, thermal modeling, and surface engineering for similar cryogenic thermal management projects. We assist clients in optimizing diamond material type, thickness (SCD/PCD up to 500 ”m), doping (BDD), and surface finish to meet stringent requirements for low heat load and superior performance in vacuum environments.

Call to Action: For custom specifications or material consultation concerning cryogenic optical shielding, advanced thermal management, or high-stability substrates for gravitational-wave applications, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

In cryogenic gravitational-wave detectors, one of the most important issues is the fast cooling of their mirrors and keeping them cool during operation to reduce thermal noise. For this purpose, the correct estimation of thermal-radiation heat transfer through the pipe-shaped radiation shield is vital to reduce the heat load on the mirrors. However, the amount of radiation heat transfer strongly depends on whether the surfaces reflect radiation rays diffusely or specularly. Here, we propose an original experiment to distinguish between diffusive and specular surfaces. This experiment has clearly shown that the examined diamond-like carbon-coated surface is specular. This result emphasizes the importance of suppressing the specular reflection of radiation in the pipe-shaped shield.